Final answer:
Option A is answer. The most likely cause for a computer not recognizing an external hard drive after a motherboard replacement is incompatible drivers.
Step-by-step explanation:
If a computer does not recognize an external hard drive after a motherboard replacement, the most likely cause is incompatible drivers. When you replace a motherboard, the new board often requires different drivers than the previous one, and if the necessary drivers aren't installed, external devices like hard drives may not be recognized. Ensuring that the drivers are up to date and compatible with your new motherboard can usually resolve this issue.
Another possibility is incorrect BIOS settings; the new motherboard's BIOS may be configured differently and not support the hard drive by default. In some cases, adjusting the settings to detect the hard drive will correct the problem. Power supply issues are less likely since an external hard drive typically gets its power from the USB or external power source, not the motherboard.
A faulty hard drive is also a possibility, but if the drive was functioning before the motherboard replacement, this is less probable unless the drive was damaged during the process.